The elastic properties of the β-HMX under an extra pressure are studied from density functional theory calculations using the projector augmented wave method. The calculated bulk modulus and shear modulus under zero pressure are 12.7 GPa and 4.4 GPa which are in good agreement with the available experimental results. A detailed analysis of the pressure-dependent stiffness tensor shows that the bulk modulus and shear modulus both increase as the pressure increases. As the pressure goes up to 7 GPa, the lattice is unstable along the direction of the shear strain. This result agrees well with the results of Raman scattering experiment.